Problem: Simplify the following expression: $\dfrac{44a^5}{55a^5}$ You can assume $a \neq 0$.
Answer: $ \dfrac{44a^5}{55a^5} = \dfrac{44}{55} \cdot \dfrac{a^5}{a^5} $ To simplify $\frac{44}{55}$ , find the greatest common factor (GCD) of $44$ and $55$ $44 = 2 \cdot 2 \cdot 11$ $55 = 5 \cdot 11$ $ \mbox{GCD}(44, 55) = 11 $ $ \dfrac{44}{55} \cdot \dfrac{a^5}{a^5} = \dfrac{11 \cdot 4}{11 \cdot 5} \cdot \dfrac{a^5}{a^5} $ $\phantom{ \dfrac{44}{55} \cdot \dfrac{5}{5}} = \dfrac{4}{5} \cdot \dfrac{a^5}{a^5} $ $ \dfrac{a^5}{a^5} = \dfrac{a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a} = 1 $ $ \dfrac{4}{5} \cdot 1 = \dfrac{4}{5} $